Population ecology III: Population growth and regulation

I. Brief overview of demography

            A. Net reproductive rate (R_o) = prob. of survival * prob. of producing offspring

                        1. R_o > 1: female is producing more than replacement, so population is increasing

                        2. R_o = 1: female is replaced herself, so population is stable

                        3. R_o < 1: female is not replacing herself, so population is declining

                        4. Phlox drumondii >> R_o = 2.4177 What does this tell you about the population?

                        5. Mud turtles >> R_o = 0.601 What does this tell you about the population?

            B. Per capita rate of increase (r) = lnR_o/T where T is generation time

                        1. T = Sxl_xm_x/ R_o >> grade point analogy

                        2. r > 0: population is growing

                        3. r = 0: population is stable

                        4. r < 0: population is declining

            C. Using this information we will build models of population growth

II. Geometric growth and exponential growth

            A. Populations exhibit these types of growth patterns when resources are abundant

            B. Geometric growth

                    1. Occurs in organisms that do not experience generation overlap >> discrete generations

                            a. Annual plants >> life cycle occurs in one year

                            b. Insects

                    2. Successive generations differ in size by a constant ratio

                    3. Geometric rate of increase >> l = N_t+1/N_t

                            a. N₁ = N₀ x l

                            b. N₂ = N₁ x l >> N₂ = N₀ x l x l = N₀ x l²

                    4. Equation for geometric growth >> N_t = N₀l^t

                            a. Constant rate of growth

                    5. Discrete model → N_t = R_o^tN_o

            C. Exponential Growth

                    1. Occurs in organisms which have overlapping generation, resulting in continuous pop. growth

                    2.  dN/dt = rN

                            a. Rate of population growth

                            b. Change in numbers over a change in time

                            c. per capita rate of increase (r) x population size

                                    1) r is constant

                                    2) N is variable

                                    3) As population size increases the rate of growth increases

                            d. N_t = N₀e^rt

                                    1) e = base of natural logarithms

                                    2) Rate increases with population

            D. Previous two models are assuming unlimited environmental resources

                        1. Unrealistic

                        2. Natural populations have the potential to increase dramatically >> remember back to

                         four basic tenets of natural selection

III. Logistic population growth

            A. Incorporates environmental limitations to population growth

            B. As a population increases, growth rate begins to slows and then ceases as pop. size levels off.

                        1. Sigmoidal (S-shaped) population growth curve

                        2. Carrying capacity (K)—the maximum number of individuals that can be supported in a

                        given area or habitat; the upper asymptote of logistic equation

            C. More realistic growth model >> variations of this have been documented in nature

            D. Some resource becomes limiting at high densities, slowing and eventually stopping pop.

                 growth

            E. dN/dt = r_mN(K-N/K)

                        1. A modified version of exponential growth model

                        2. Slows growth as population nears K

                        3. Logistic equation

                        4. r_m = max. per capita rate of increase under ideal environmental conditions

                                    a. Intrinsic rate of increase—the potential rate of growth of a pop. in an infinite

                                       environment

                                    b. r = lnR₀/T

                                                1) Realized per capita rate of increase is what we calculated in demography

                                                2) Generally less than r_m

          F. dN/dt = r_mN(K/K-N/K) >> dN/dt = r_mN(1-N/K)

                       1. dN/dt slows as N increases

                       2. 1-N/K >> becomes a smaller decimal fraction until reaching zero (N=K)

                       3. Logistic growth becomes a smaller fraction of exponential growth rate

                       4. N/K = “environmental resistance” to population growth

                       5. r = r_m(1-N/K) depends on population size

                                 a. When N is low (1 – N/K) is close to 1 >> r = r_m >> dN/dt = rN

                                 b. r = b – d (b = birth rate, d = death rate)

                                 c. Linear relationship between r and N

            G. When a population reaches K its growth rate and size don’t remain static

                        1. Population oscillates around K

                        2. Resources fluctuate over time

            H. Populations may also go extinct if population size is below a certain size

                        1. A minimum population size needed in order to grow

                        2. Below minimum population decreases until extinct

                        3. Factors leading to this needed minimum population size

                                    a. Difficult to find reproductively active mate >> spread out over greater area

                                    b. Greater chance of an individual succumbing to predation

                        4. Allee effect

IV. Limits to population growth

            A. Environment limits population growth by influencing birth and death rates

            B. Three basic types of response to growth

                        1. Levels off and then fluctuates above and below K >> stability governed by intrinsic

                           influences

                        2. Population fluctuates widely without reference to equilibrium size >> influenced by

                            extrinsic factors, such as weather

                        3. Population may ocscillate between high and low points with some regularity between

                            highs and lows

            C. Numerous factors not only limit population growth but also size

                        1. Carrying capacity (K) is determined by both intrinsic and extrinsic factors

                        2. Density-dependent factors (d-d)—factors whose influence changes with density

                                    a. Biotic factors—environmental factors resulting from the activities of living

                                        organisms

                                    b. Predation

                                    c. Competition

                                    d. Disease

                                    e. Only these types of factors result in population regulation

                        3. Density-independent factors (d-I)—any environmental factor affecting density, the

                            influence of which is independent of density

                                    a. Abiotic factors—physical, chemical, and other nonliving environmental factors

                                    b. Weather events

                                    c. These do not regulate populations about an equilibrium size

                        4. Populations are affected by a variety of both kinds of factors

                                    a. Sometimes density-dependent factors predominate

                                    b. Sometimes density-indendent factors predominate

            D. May be more informative to talk about factors from the point of view of the population

                        1. Extrinsic influences—those outside of the population

                                    a. Weather >> probably most powerful (density-independent)

                                    b. Human activity (either density-dependent or density-independent)

                                    c. Resource availability >> largely through intraspecific competition (d-depend)

                                    d. Diseases and parasites

                                                1) Density-dependent

                                                2) Density-independent when introduced to a population with no resistance

                                    e. Predation >> density-dependent

                        2. Instrinsic influences—those influences imposed by the population itself

                                    a. Crowding (disease virulence)

                                    b. Behavior  >> territoriality and social dominance

                                    c. Dispersal

V. Body size and population growth

            A. Inverse relationship between body size and intrinsic rate of growth

            B. Small organisms reproduce faster >> populations increase quicker

            C. Large animals reproduce at a slower rate >> populations increase more slowly